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Q.
A bacterium divides every $35$ minutes. If a culture containing $105$ cells/mL is grown for $175$ minutes, what will be the cell concentration/mL after $175$ minutes?
Total number of bacteria produced $=2^{n}$
$n=\frac{\text { Total time }}{\text { Time of division }}=\frac{175}{35}=5$
Thus, after $5$ divisions total number of bacteria will be $2^{5}=32$. Initially there are $10^{5}$ bacteria/mL and therefore, after $175$ minutes, the concentration of bacterial cells will be $32 \times 10^{5}$ or $3.2 \times 10^{6} cells / mL$.